Drag and Torque on Locked Screw Propeller

Transcription

1 the International Journal on Marine Navigation and Safety of Sea Transportation Volume 8 Number 3 September 24 DOI:.276/ Drag and Torque on Locked Screw Propeller T. Tabaczek Wrocław University of Technology, Wrocław, Poland T. Bugalski Ship Design and Research Centre CTO S.A, Gdańsk, Poland ABSTRACT: Few data on drag and torque on locked propeller towed in water are available in literature. Those data refer to propellers of specific geometry (number of blades, blade area, pitch and skew of blades). The estimation of drag and torque of an arbitrary propeller considered in analysis of ship resistance or propulsion is laborious. The authors collected and reviewed test data available in the literature. Based on collected data there were developed the empirical formulae for estimation of hydrodynamic drag and torque acting on locked screw propeller. Supplementary CFD computations were carried out in order to prove the applicability of the formulae to modern moderately skewed screw propellers. INTRODUCTION In some modes of ship operation or maintenance the propeller shaft is immobilised and propeller becomes locked. The case of fast ships fitted with multipleengine and multiple propeller propulsion system with three or four propellers is discussed by Charchalis []. Such ships sometimes operate at high speed but often sail at reduced or cruising speed. Excessive engines are stopped and passive propellers are locked in order to prevent the gear and engine from wear or failure. Charchalis proposed the method for evaluating the drag and hydrodynamic torque on locked propeller. The method is based on thrust and torque coefficients from four quadrant open water characteristics of considered screw propeller. In example calculations Charchalis refers to diagrams for three bladed screw propellers presented in [2]. Propellers may also stay locked when ship is towed in emergency or in the course of delivery from shipyard to ship operator. Then the concern is to protect the gear and engine, and despite the additional drag during towing the propeller shaft may be intentionally immobilized. All modern sailboats, with except for the smallest ones, are equipped with mechanical propulsion. When sailing the engine is stopped and some sailors decide to lock the shaft and propeller, sometimes due to the mistaken belief that locked propeller is more favourable for low drag. (The question of whether the drag of the locked propeller is lower than the drag of the windmilling propeller was argued as late as in 22.) Sometimes the manufacturers of small marine gearboxes specify that the shaft should be locked when the engine is stopped and the vessel is in motion, because some gearboxes receive adequate lubrication only when the engine is running. Although some test results of hydrodynamic drag and torque acting on locked screw propeller are available in open literature and one may refer to them directly, it would be more convenient for ship designers and operators to have a simple formula ready to apply and provide the estimation of drag and torque instantly. The present authors have 44

2 reviewed and compared the available test data. Based on a simple assumption of negligible effect of interaction between blades in the case of locked propeller they proposed the empirical formulae for estimation of drag and torque on locked screw propeller in open water. The research was extended with CFD computations in order to confirm the applicability of developed formulae to modern moderately skewed propellers. The allowances to drag and torque were proposed in such cases. astern (VA<; n<), as well as the crashback (VA>; n<) and crashahead (VA<; n>) conditions. The problem of two different systems of coefficients has been overcome by application of advance angle β and non dimensional coefficients based on speed of blade section at radius r=.7r across the water Vr = [VA 2 + (.7πnD) 2 ] /2 [4]: β = arc tan(va /.7πnD) = T / {.5ρ [VA 2 + (.7πnD) 2 ] π/4 D 2 } (3) 2 NON DIMENSIONAL COEFFICIENTS The results of open water tests of marine screw propellers are presented in the form of nondimensional coefficients of speed, thrust and torque. Usually, in standard range of ahead speed and ahead rotation, the advance coefficient J, thrust coefficient KT and torque coefficient KQ are defined as J = VA / (nd) KT = T / (ρn 2 D 4 ) () KQ = Q / (ρn 2 D 5 ) where: VA advance speed of propeller n rotational rate D propeller diameter T propeller thrust Q torque ρ density of water. When screw propellers are tested in extended range of operating conditions, and when rotational sped equals zero or is close to zero, the values of conventional coefficients KT and KQ approach infinity, and non dimensional coefficients must be defined otherwise in order to present the finite performance. [3] and [2] applied the conventional coefficients () around bollard conditions and modified coefficients: J = nd / VA = /J KT = T / (ρva 2 D 2 ) (2) KQ = Q / (ρva 2 D 3 ) = Q / {.5ρ [VA 2 + (.7πnD) 2 ] π/4 D 3 } (Similar idea by Lavrentiev, based on reference speed (VA 2 + n 2 D 2 ) /2, was noticed but not used in [2].) Performance characteristics (β) and (β) are single valued, continuous and periodical, and more suitable for theoretical investigation of ship manoeuvres. In the following analysis only the thrust and torque at n= are considered and the authors use the coefficients and at β=π/2. The modified thrust and torque coefficients KT and KQ needed conversion according to the following correspondence (valid only at n=): = KT / (π/8) = KQ / (π/8) 3 AVAILABLE TEST DATA In 948 [3] described model tests carried out in order to determine open water performance of screw propellers in all regimes of operation (in four quadrants of operating conditions). Tests were carried out with a series of four bladed propellers of blade area ratio equal to.45. The only parameter differing propellers in the series was the pitch ratio that varied from zero to.6. presented the results in the form of non dimensional coefficients plotted against advance ratio. He applied two systems of coefficients: the conventional one based on rotational speed n (Eq. ()) and the modified one based on advance speed VA (Eq. (2)). ( applied different symbols but the same definitions as used in this paper.) Values of coefficients at n= were converted and shown in Fig.. around locked conditions (n=). (Different symbols are used across the literature for modified coefficients.) The open water four quadrant hydrodynamic characteristics of each screw propeller were presented in [2] and [3] using at the same time two systems of coefficients with overlapping ranges of advance coefficient far from bollard and locked conditions. The definition of advance coefficient J implies that it does not define the operating conditions uniquely, and additional information is necessary do distinguish the ahead (VA>; n>) and 442

3 -,5,2,4,6,8,2,4,6,8 -, -,5 -,2 -,25 -,3 -,35 -,4 -,45 -,5 -,2 -,3 -,4 -,5 -,6 -,7,2,4,6,8,2,4,6,8 -, Figure. Thrust and torque coefficients of four bladed propellers tested by [3], n= In 954 through 956 [2] carried out model tests with a series of three bladed screw propellers. The series included propellers with three values of blade area ratio AE/A:.5,.8 and.. For each value of AE/A the pitch ratio varied in the range.6.6. In [2] the results were presented in diagrams, using two systems of coordinates defined by formulae () and (2). Values of coefficients at n= were converted and are shown in Fig. 2. The results for AE/A=. read out from the tangle of lines in the original diagrams [2] are highly irregular and were omitted in the following analysis.,2,4,6,8,2,4,6,8 -, -,2 -,3 -,4 -,5 -,6 -,7 -,8 -,4 -,6 -,8 -, -,2 -,4,2,4,6,8,2,4,6,8 -,2 AE/A=.5 AE/A=.8 AE/A=.5 AE/A=.8 Figure 2. Thrust and torque coefficients of three bladed propellers tested by [2], n= In 969 van Lammeren et al. [4] presented fourquadrant hydrodynamic characteristics of 4 screw propellers selected from the well-known B-series. The selection was made so that the effect of three basic parameters (namely, A E /A and the number of blades z) on performance in all regimes of operation was revealed. Basic parameters of individual propellers are given in Table. The measured thrust and torque were converted into non-dimensional coefficients C T * and C Q * according to the definition (3) and presented in diagrams. Van Lammeren et al. [4] proposed also the approximation of characteristics with the Fourier series of 2 terms, convenient for ship manoeuvring study. However, some coefficients of Fourier series given in [4] do not allow reproducing the corresponding curves presented in diagrams. In order to determine the values of thrust and torque coefficients at n= (β=π/2) the present authors used the approximation of characteristics with Fourier series of 3 terms reprinted in report [5]. Calculated values of coefficients are listed in Table and shown in Fig. 3. Table. Propellers from B series tested in four quadrants [3] Propeller z AE/A B B B B B B B B B B B B B B ,2 -,3 -,4 -,5 -,6 -,7 -,8 -,9 B4-7 -,,2,4,6,8,2,4,6 -,4 -,6 -,8 -, -,2 -,4 -,6 B4-7,2,4,6,8,2,4,6 -,2 443

4 /Z /Z -,4 -,6 -,8 - -,2 B4-4, B4-55, B4-7, B4-85, B4-,,2,4,6,8,,2 -,2 -,4 -,6 -,8 -, -,2 -,4 -,6 -,8 AE/A B4-4, B4-55, B4-7, B4-85, B4- -,2,,2,4,6,8,,2 -,5 -, -,5 -,2 -,25 AE/A B3-65, B4-7, B5-75, B6-8, B7-85,5,,5,2,25 (AE/A)/Z B3-65, B4-7, B5-75, B6-8, B7-85,5,,5,2,25 -,5 -, -,5 -,2 /Z /Z Table 2. Sailboat fixed blade propellers tested by Lurie and Taylor [6] Propeller Campbell Campbell Michigan Michigan Sailer Sailer Wheel Wheel 2 bladed 3 bladed 2 bladed 3 bladed z D [m] AE/A (AE/A)/z MacKenzie and Forrester [7] measured drag of another three 2 inch sailboat propellers. Results were presented in the form of drag plotted against speed. Particulars of propellers along with calculated values of thrust coefficient (torque was not reported in original paper) at speed VA of 3.9 m/s are summarized in Table 3. Table 3. Sailboat fixed blade propellers tested by MacKenzie and Forrester [7] Propeller A B C z D [m] AE/A (AE/A)/z, In 23 Dang et al. [8] presented the outcomes from open water model tests of 4 bladed controllable pitch propellers denoted C4 4, from the newly developed Wageningen C series. There were 4 modern moderately skewed propellers designed according the best design practice. The propellers differed from each other with the design pitch ratio that was equal to.8,.,.2 and.4. The performance of propellers was measured in two quadrants of operation including n=. Test data were presented in the form of thrust and torque coefficients and plotted in diagrams against advance angle β. -,25 -,3 -,35 (AE/A)/Z Figure 3. Thrust and torque coefficients of propellers from B series [4], n= Lurie and Taylor [6] investigated performance characteristics of 2 and 3 bladed 3 inch commercially available propellers designed for use on small and medium size sailboats. Besides the nonconventional screw propellers (folding or feathering propellers) the four fixed blade propellers were tested. The performance at forward speed was measured including propeller drag at n=. Results were presented in the form of drag plotted against advance speed. Particulars of propellers along with values of thrust coefficient (torque was not reported in original paper) at speed VA above 3. m/s are summarized in Table 2. 4 EMPIRICAL FORMULAE For engineering applications the drag and torque of a locked propeller should be calculated using only basic parameters of propeller that are usually available, i.e. propeller diameter, number of blades, blade area ratio and pitch ratio. The available values of thrust and torque coefficients were used to determine the relationships between drag/torque and basic parameters of propeller.. The relations between drag/torque and pitch ratio have been determined based on data from [2], [3] and [4]. The values of thrust and torque coefficients were normalised using the values for =. (see Fig. 4). Using the least square approximation the relation between the normalised thrust coefficient CTn* and was fitted with function, and the relation between the normalised torque coefficient CQn* and with quadratic polynomial: 444

5 CTn*=,3 +,3 (4) CQn* =,3 () 2 +,35,5 The relations between coefficients and and become as follows: = (=.) (,3 +,3) (5) /Z,5,,5,2,25,3 -,5 -, -,5 -,2 -,25 B-series sailboat props approx. = (=.) (,3 () 2 +,35,5) -,3 (AE/A)/Z CTn*,4,2,8,6,4,2,2,4,6,8,2,4,6,8,6,4.5.8 B4-7 approx. /Z -,5,5,,5,2,25,3 -, -,5 -,2 -,25 -,3 -,35 -,4 (AE/A)/Z B-series approx. Figure 5. Relation between the thrust and torque coefficients per one blade (/z and /z) and unit blade area ratio (AE/A)/z, at =. CQn*,2,8,6,4,2,2,4,6,8,2,4,6,8.5.8 B4-7 approx. Because the data for two and three bladed propellers from [2], [6] and [7] do not align with other data, the least square approximation was fitted using only data for B series [4] and those given by [3]. For =. the following formulae are proposed: (=.)/z = 4,28 [(AE/A)/z] 2 2,6 (AE/A)/z +,3 (6) Figure 4. Variation of the normalized thrust and torque coefficients with pitch ratio The assumption of negligible interaction between blades in the case of n= allowed to consider the force or torque on a single blade instead on entire propeller. Two basic parameters i.e. blade area ratio and number of blades were combined into a single parameter, namely the area ratio of a single blade (AE/A)/z. The relationship was investigated using data for propellers with =., an average value encountered in design of merchant ships. Much data were available directly without the need for extrapolation from other values of pitch ratio. Only the coefficients for sailboat propellers from [6] and [7] were extrapolated using the relationship (5). The values of thrust and torque coefficients per one blade were collected and presented in Fig. 5. (=.)/z =,796 [(AE/A)/z] 2,453 (AE/A)/z +,26 Combining the approximations (6) and (5) the empirical formulae for 4 to 7 bladed propellers becomes as follows: = z {4,28 [(AE/A)/z] 2 2,6 (AE/A)/z +,3} (,3 +,3) (7) = z {,796 [(AE/A)/z] 2,453 (AE/A)/z +,26} (,3 () 2 +,35,5) The fit of approximation (7) to empirical data is illustrated in Fig

6 - (eq.(7)),2,8,6,4,2,2,4,6,8,2 - (test data),2,6 Nordstroem van Lammeren sailboat props (7)= (test) characteristics ( < J < J(KT=)). The CFD computations have not been verified and validated at locked conditions (at n=). The results of computations in the form of nondimensional coefficients are included in Table 4, in comparison to values calculated using the formulae (7). The fit of approximation is illustrated in Fig. 7 where approximated values are compared to results of CFD computations and to test data in the case of controllable pitch propellers C4 4 [8]. Approximated values are underestimated by approximately 5 to 5 per cent in relation to both CFD and test data.,2 - (eq.(7)),2,8,4,4,8,2,6,2 - (test data) Nordstroem van Lammeren (7)= (test) Figure 6. The fit of approximation (7) to empirical data - (eq.(7)),8,6,4,2,2,4,6,8,2 - (CFD),2 P62 CP469 P P2 P9 C4-4 (test data) (eq.(7))=(cfd),6 5 CFD COMPUTATIONS In order to assess the applicability of empirical formulae to modern moderately skewed propellers a number of RANSE CFD computations was carried out using ready geometries and grids previously used for computations of propeller flow in forward operating conditions [9], []. Main particulars of propellers are collected in Table 4. Table 4. Propellers used in CFD computations KP55 CP469 P P2 P9 (KCS) (Nawigator) z D [mm] P.7/D AE/A rake [mm] (AE/A)/z skew back ,33 ratios(r)/d skew angle θs(r) [deg] CFD eq. (7) ( 5 %) ( 9 %) (+ %) ( 7 %) ( 3 %) CFD eq. (7).29, ( 5 %) ( 5 %) (+9 %) ( 5 %) ( 4 %) Computations were carried out using the commercial CFD software CDadapco STAR CCM+. High accuracy of CFD computations using that software and appropriate grids has been proved for computations of flow around screw propellers operating in the conventional range of open water - (eq.(7)),2,8,4,4,8,2,6,2 - (CFD) P62 CP469 P P2 P9 C4-4 (test data) (eq.(7))=(cfd) Figure 7. The fit of approximation (7) to CFD and test data 6 CONCLUSIONS Using the available test data for locked screw propellers the formulae (7) for estimation of thrust and torque coefficients and (defined by eq. (3)) are proposed. The coefficients are related to the basic parameters of propeller, namely to pitch ratio, blade area ratio and the number of blades. The formulae are valid principally for non skewed or low skewed screw propellers, in the range of pitch ratio from.6 to.6 and in the range of single blade area ratio (AE/A)/z from. to.25. In application to 2 or 3 bladed propellers the approximated values of drag and torque may be overestimated by up to 3% in relation to actual forces (Fig.6). In the case of moderately skewed propellers the approximated values may be underestimated. Based on the outcomes from CFD computations the authors propose the allowance of +6 %. Known the drag and torque coefficients, the drag and torque on locked screw propeller are estimated according to the formulae: 446

7 D = T =.25 ρva 2 πd 2 Q =.25 ρva 2 πd 3 using the relevant advance speed. It is proposed to use the average velocity of flow in nominal wake of ship: VA = VS( wn) where VS denotes ship speed, and wn the nominal wake fraction. REFERENCES [] A. Charchalis: Resistance of idle propellers in marine multi propeller propulsion systems, Journal of KONES Powertrain and Transport, Vol. 7, No. 4, 2 [2] A.M. Basin, I.Ya. : Theory and calculation of screw propellers, Sudostroienie, Leningrad, 963 (in Russian) [3] H.F. Nordström: Screw propeller characteristics, Publ. No.9, SSPA, 948 [4] W.P.A. van Lammeren, J.D. van Manen, M.W.C. Oosterveld: The Wageningen B screw series, Trans. SNAME, 969 [5] R.F. Roddy, D.E. Hess, W. Faller: Neural network predictions of the 4 quadrant Wageningen propeller series, Naval Surface Warfare Center Carderock Division, Hydromechanics Department Report NSWCCD 5 TR 26/4, April 26 [6] B. Lurie, T. Taylor: Comparison of ten sailboat propellers, Marine Technology, 32, pp.29 25, 995 [7] P.M. MacKenzie and M.A. Forrester: Sailboat propeller drag, Ocean Engineering, 35 (), pp.28 4, 28 [8] J. Dang, H. J. J. van den Boom, J. Th. Ligtelijn: The Wageningen C and D Series Propellers, 2th International Conference on Fast Sea Transportation FAST 23, Amsterdam, 2 5 December 23 [9] T. Bugalski, and P. Hoffmann: Numerical Simulation of the Interaction between Ship Hull and Rotating Propeller, Proceedings of Workshop on Numerical Ship Hydrodynamics Gothenburg 2, Gothenburg, Sweden, 2 [] T. Bugalski, P. Hoffmann: Numerical Simulation of the Self Propulsion Model Tests, Second International Symposium on Marine Propulsors smp, Hamburg, Germany, June 2 447